Re: fixed point vs floating point

[dewar@merv.cs.nyu.edu (Robert Dewar)]

Matthew says

<<Remember that thread a few months back about floating point comparison?  As
Robert reminded us, you have to know what you're doing when you use
floating point arithmetic.  I was trying to avoid floating point types,
because I'm not a numerical analyst, and don't want to just *hope* my
floating point calculations produce a correct result.  I want to *know*
they're correct.  My error analysis is simpler if use a fixed point type,
right?

If my abstraction calls for a real type having an absolute error and not a
relative error, then clearly a fixed point type is called for, even if it's
less efficient, right?  Isn't it always true that we should code for
correctness first, by using a type that directly models the abstraction,
and then optimize only if necessary?  Are you making an exception to this
rule for fixed point types?>>


When Robert was reminding you that you need to know what you are doing
when using Floating-Point arithmetic, he did not for a moment mean to say
that somehow the problem is trivial in fixed-point arithmetic. Computing
trig functions in limited precision fixed-point and retaining sufficient
accruacy is a VERY hard problem.

Note that neither fixed-point nor floating-point models the abstraction,
since the abstraction is real! The only difference is whether the error
control is relative or absolute. FOr some purposes relative error is
*easier* to analyze than *absolute* error, but there is no sense in which
fixed-point is somehow a more accurate abstract representation of real
than flaoting-point!